-4=64a^2/4a eching

$$- 4 = \frac { 64 a ^ { 2 } } { 4 a }$$

a uchun yechish

$$a=-\frac{1}{4}=-0,25$$

Faktorlash qadamlari

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4a ga ko'paytirish.

$$-16a=64a^{2}$$

Ikkala tarafdan 64a^{2} ni ayirish.

$$-16a-64a^{2}=0$$

a omili.

$$a\left(-16-64a\right)=0$$

Tenglamani yechish uchun a=0 va -16-64a=0 ni yeching.

$$a=0 a=-\frac{1}{4}$$

a qiymati 0 teng bo‘lmaydi.

$$a=-\frac{1}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4a ga ko'paytirish.

$$-16a=64a^{2}$$

Ikkala tarafdan 64a^{2} ni ayirish.

$$-16a-64a^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-64a^{2}-16a=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -64 ni a, -16 ni b va 0 ni c bilan almashtiring.

$$a=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}}}{2\left(-64\right)}$$

\left(-16\right)^{2} ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-16\right)±16}{2\left(-64\right)}$$

-16 ning teskarisi 16 ga teng.

$$a=\frac{16±16}{2\left(-64\right)}$$

2 ni -64 marotabaga ko'paytirish.

$$a=\frac{16±16}{-128}$$

a=\frac{16±16}{-128} tenglamasini yeching, bunda ± musbat. 16 ni 16 ga qo'shish.

$$a=\frac{32}{-128}$$

\frac{32}{-128} ulushini 32 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$a=-\frac{1}{4}$$

a=\frac{16±16}{-128} tenglamasini yeching, bunda ± manfiy. 16 dan 16 ni ayirish.

$$a=\frac{0}{-128}$$

0 ni -128 ga bo'lish.

$$a=0$$

Tenglama yechildi.

$$a=-\frac{1}{4} a=0$$

a qiymati 0 teng bo‘lmaydi.

$$a=-\frac{1}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4a ga ko'paytirish.

$$-16a=64a^{2}$$

Ikkala tarafdan 64a^{2} ni ayirish.

$$-16a-64a^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-64a^{2}-16a=0$$

Ikki tarafini -64 ga bo‘ling.

$$\frac{-64a^{2}-16a}{-64}=\frac{0}{-64}$$

-64 ga bo'lish -64 ga ko'paytirishni bekor qiladi.

$$a^{2}+\left(-\frac{16}{-64}\right)a=\frac{0}{-64}$$

\frac{-16}{-64} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$a^{2}+\frac{1}{4}a=\frac{0}{-64}$$

0 ni -64 ga bo'lish.

$$a^{2}+\frac{1}{4}a=0$$

\frac{1}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{8} olish uchun. Keyin, \frac{1}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}+\frac{1}{4}a+\left(\frac{1}{8}\right)^{2}=\left(\frac{1}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{8} kvadratini chiqarish.

$$a^{2}+\frac{1}{4}a+\frac{1}{64}=\frac{1}{64}$$

a^{2}+\frac{1}{4}a+\frac{1}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a+\frac{1}{8}\right)^{2}=\frac{1}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a+\frac{1}{8}\right)^{2}}=\sqrt{\frac{1}{64}}$$

Qisqartirish.

$$a+\frac{1}{8}=\frac{1}{8} a+\frac{1}{8}=-\frac{1}{8}$$

Tenglamaning ikkala tarafidan \frac{1}{8} ni ayirish.

$$a=0 a=-\frac{1}{4}$$

a qiymati 0 teng bo‘lmaydi.

$$a=-\frac{1}{4}$$